In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, inequalities, monotony Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential equations those approached in stability point view. literature, Fredholm, Volterra Hammerstein integrals symmetric kern...

This study is devoted to solve the Chandrasekhar integral equation that it used for modeling problems in theory of radiative transfer a plane-parallel atmosphere, and others research areas like kinetic gases, neutron transport, traffic model, queuing among others. First all, we transform into nonlinear Hammerstein-type with corresponding Nemystkii operator proper nonseparable kernel. Them, appr...

In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions. Also, effect of noise shows our solutions ...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

Keywords: Analytic semigroup Banach fixed point theorem Caputo derivative Faedo–Galerkin approximations Nonlocal conditions Neutral fractional differential equation a b s t r a c t This paper is concerned with the approximation of the solution for neutral fractional differential equation with nonlocal conditions in an arbitrary separable Hilbert space H. We study an associated integral equation...